Skip to main content

Full text of "Analytical Mechanics"

See other formats

196                      ANALYTICAL MECHANICS
presupposes work by or against external forces, which in its turn presupposes interaction with external bodies. But since no external forces are supposed to act upon the system, there cannot be interaction with external bodies or exchange of energy.
164.   The Principle of the Conservation of Energy.  One of the greatest achievements of the nineteenth century was the recognition and the experimental verification of the great generalization known as the principle of the conservation of energy, which states that the total amount of energy of an isolated system is constant.
By means of the interaction of the different parts of an isolated system the various forms of its energy may be changed into other forms, and the distribution of the energy within the system may be altered, but the total amount of energy remains constant. In other words, energy may be transformed or transferred but cannot be annihilated or created.
165.   Dynamical Energy.  Kinetic and potential forms of energy are called dynamical energy.    The distinction between dynamical and nondynamical energy, such as heat energy, chemical energy, etc., is a matter of convenience. Heat energy may be treated as kinetic energy, but in order to do that molecules and their individual motions have to be taken into account.    On the other hand chemical energy may be treated as potential energy if molecular and atomic forces can be taken into account.    It is to avoid the complications of the molecular structure of bodies that these forms of energy are considered as nondynamical.
166.   Conservation of  Dynamical Energy.  When all  the forces acting within an isolated system are  conservative the interchange of energy is confined to the potential and kinetic forms of the energy of the system.    Therefore applying the general principle of the conservation of energy we see that in such a system the sum of the dynamical energy remains constant, that is,
T+U= const.                            (IX)